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The immediate graph that springs to mind is a sine graph, except this new graph has two transformations: a stretch scale factor 5 in the y direction because the peaks are reaching 5 and -5 and then the second is a shift along the x axis. This means the equation of our new graph will be of the form:
y = ksin(x+c)
where k is the s.f. of the stretch and c is the shift along the x axis.
k is simple, it is 5. In a normal sine graph the peaks are at 1 now they are at 5.
y = 5sin(x+c)
Now we need to find c. From observation it is clear that the graph passes through the point (0,4) so we can sub these values in an solve c.
4 = 5sin(0+c)
sin(c) = 4/5
c = arcsin(4/5)
So adding this value to are equation we can reach the final answer of:
y = 5sin(x+arcsin(4/5)